Phylogenomics is fundamentally altering our understanding of the taxonomy, systematics and biogeography of scleractinian corals. Recently-developed phylogenomic techniques provide a path for resolving species-level relationships in diverse and ecologically-important groups such as Acropora, while also revealing that many morphological characters traditionally used to define species are not informative. Here, we use targeted capture of conserved loci to investigate systematic relationships within a clade of Acropora that contains the putatively widespread ‘lab rat’ species A. tenuis and related species. Maximum likelihood phylogenies and clustering of SNPs from specimens collected across the Indo-Pacific and harvested genomes indicate the presence of at least ten distinct species, only four of which correspond to currently accepted species, with the remainder either undescribed or nominal species synonymised incorrectly. Based on molecular, morphological and geographic evidence, we describe two new species (Acropora rongoi n. sp. and Acropora tenuissima n. sp.), and remove Acropora kenti (Brook 1892) from eastern Australia out of synonymy with A. tenuis (Dana 1846). Our molecular phylogeny is incongruent with species boundaries and evolutionary relationships assumed using traditional morphological taxonomy, and reveals that both species diversity and geographic structure are far greater than currently assumed, a finding with important implications for ecology and conservation.